2(s+3)4s-5s=148

Solution for 2(s+3)4s-5s=148 equation:

Simplifying
2(s + 3) * 4s + -5s = 148

Reorder the terms:
2(3 + s) * 4s + -5s = 148

Reorder the terms for easier multiplication:
2 * 4s(3 + s) + -5s = 148

Multiply 2 * 4
8s(3 + s) + -5s = 148
(3 * 8s + s * 8s) + -5s = 148
(24s + 8s2) + -5s = 148

Reorder the terms:
24s + -5s + 8s2 = 148

Combine like terms: 24s + -5s = 19s
19s + 8s2 = 148

Solving
19s + 8s2 = 148

Solving for variable 's'.

Reorder the terms:
-148 + 19s + 8s2 = 148 + -148

Combine like terms: 148 + -148 = 0
-148 + 19s + 8s2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-18.5 + 2.375s + s2 = 0

Move the constant term to the right:

Add '18.5' to each side of the equation.
-18.5 + 2.375s + 18.5 + s2 = 0 + 18.5

Reorder the terms:
-18.5 + 18.5 + 2.375s + s2 = 0 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + 2.375s + s2 = 0 + 18.5
2.375s + s2 = 0 + 18.5

Combine like terms: 0 + 18.5 = 18.5
2.375s + s2 = 18.5

The s term is 2.375s.  Take half its coefficient (1.1875).
Square it (1.41015625) and add it to both sides.

Add '1.41015625' to each side of the equation.
2.375s + 1.41015625 + s2 = 18.5 + 1.41015625

Reorder the terms:
1.41015625 + 2.375s + s2 = 18.5 + 1.41015625

Combine like terms: 18.5 + 1.41015625 = 19.91015625
1.41015625 + 2.375s + s2 = 19.91015625

Factor a perfect square on the left side:
(s + 1.1875)(s + 1.1875) = 19.91015625

Calculate the square root of the right side: 4.462079812

Break this problem into two subproblems by setting 
(s + 1.1875) equal to 4.462079812 and -4.462079812.

Subproblem 1
s + 1.1875 = 4.462079812

Simplifying
s + 1.1875 = 4.462079812

Reorder the terms:
1.1875 + s = 4.462079812

Solving
1.1875 + s = 4.462079812

Solving for variable 's'.

Move all terms containing s to the left, all other terms to the right.

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + s = 4.462079812 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + s = 4.462079812 + -1.1875
s = 4.462079812 + -1.1875

Combine like terms: 4.462079812 + -1.1875 = 3.274579812
s = 3.274579812

Simplifying
s = 3.274579812

Subproblem 2
s + 1.1875 = -4.462079812

Simplifying
s + 1.1875 = -4.462079812

Reorder the terms:
1.1875 + s = -4.462079812

Solving
1.1875 + s = -4.462079812

Solving for variable 's'.

Move all terms containing s to the left, all other terms to the right.

Add '-1.1875' to each side of the equation.
1.1875 + -1.1875 + s = -4.462079812 + -1.1875

Combine like terms: 1.1875 + -1.1875 = 0.0000
0.0000 + s = -4.462079812 + -1.1875
s = -4.462079812 + -1.1875

Combine like terms: -4.462079812 + -1.1875 = -5.649579812
s = -5.649579812

Simplifying
s = -5.649579812

Solution
The solution to the problem is based on the solutions
from the subproblems.
s = {3.274579812, -5.649579812}